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Classical Mechanics

Range

The total horizontal distance traveled by a projectile from launch to landing at the same vertical height.

Governing formula R = (v0² sin 2θ) / g
SI unit m

In depth

Ignoring air drag, maximum horizontal range for a given launch speed v0 is achieved at a launch angle θ = 45°. Complementary launch angles (θ and 90°-θ) yield identical range.

Examples in the real world

A golfer choosing a 45-degree angle to maximize drive distance across a fairway.